Newform orbit 1476.2.bb.c

• Label: 1476.2.bb.c
• Level: $1476$
• Weight: $2$
• Character orbit: 1476.bb
• Analytic conductor: $11.786$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1476.bb (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(11.7859193383\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(6\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 20 q^{7}+O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
433.1		0			0			0		−2.50819	+	1.82231i		0		−4.63580	−	1.50626i		0			0			0
433.2		0			0			0		−1.79641	+	1.30516i		0		0.950821	+	0.308940i		0			0			0
433.3		0			0			0		−0.839079	+	0.609627i		0		0.0669459	+	0.0217520i		0			0			0
433.4		0			0			0		0.839079	−	0.609627i		0		0.0669459	+	0.0217520i		0			0			0
433.5		0			0			0		1.79641	−	1.30516i		0		0.950821	+	0.308940i		0			0			0
433.6		0			0			0		2.50819	−	1.82231i		0		−4.63580	−	1.50626i		0			0			0
865.1		0			0			0		−0.979065	+	3.01325i		0		−2.13940	+	2.94464i		0			0			0
865.2		0			0			0		−0.554448	+	1.70642i		0		1.99688	−	2.74847i		0			0			0
865.3		0			0			0		−0.109008	+	0.335491i		0		−1.23945	+	1.70595i		0			0			0
865.4		0			0			0		0.109008	−	0.335491i		0		−1.23945	+	1.70595i		0			0			0
865.5		0			0			0		0.554448	−	1.70642i		0		1.99688	−	2.74847i		0			0			0
865.6		0			0			0		0.979065	−	3.01325i		0		−2.13940	+	2.94464i		0			0			0
1009.1		0			0			0		−2.50819	−	1.82231i		0		−4.63580	+	1.50626i		0			0			0
1009.2		0			0			0		−1.79641	−	1.30516i		0		0.950821	−	0.308940i		0			0			0
1009.3		0			0			0		−0.839079	−	0.609627i		0		0.0669459	−	0.0217520i		0			0			0
1009.4		0			0			0		0.839079	+	0.609627i		0		0.0669459	−	0.0217520i		0			0			0
1009.5		0			0			0		1.79641	+	1.30516i		0		0.950821	−	0.308940i		0			0			0
1009.6		0			0			0		2.50819	+	1.82231i		0		−4.63580	+	1.50626i		0			0			0
1261.1		0			0			0		−0.979065	−	3.01325i		0		−2.13940	−	2.94464i		0			0			0
1261.2		0			0			0		−0.554448	−	1.70642i		0		1.99688	+	2.74847i		0			0			0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
41.f	even	10	1	inner
123.l	odd	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1476.2.bb.c	✓	24
3.b	odd	2	1	inner	1476.2.bb.c	✓	24
41.f	even	10	1	inner	1476.2.bb.c	✓	24
123.l	odd	10	1	inner	1476.2.bb.c	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1476.2.bb.c	✓	24	1.a	even	1	1	trivial
1476.2.bb.c	✓	24	3.b	odd	2	1	inner
1476.2.bb.c	✓	24	41.f	even	10	1	inner
1476.2.bb.c	✓	24	123.l	odd	10	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T5^24 + 12*T5^22 + 133*T5^20 + 1349*T5^18 + 13805*T5^16 + 43719*T5^14 + 277643*T5^12 + 1033922*T5^10 + 2137331*T5^8 + 132500*T5^6 + 2689110*T5^4 + 542225*T5^2 + 42025